Brezis–Lieb lemma

In the mathematical field of analysis, the Brezis–Lieb lemma is a basic result in measure theory. It is named for Haïm Brézis and Elliott Lieb, who discovered it in 1983. The lemma can be viewed as an improvement, in certain settings, of Fatou's lemma to an equality. As such, it has been useful for the study of many variational problems.